Nature of logic and perception essay

Birkhoff and von Neumann remarked on this fact in their paper: “[...] whereas logicians have usually assumed that properties of negation were the ones least able to withstand a critical analysis, the study of mechanics points to the distributive identities as the weakest link in the algebra of logic.” And concluded that “the propositional calculus of quantum mechanics has the same structure as an abstract projective geometry.” However, L(H) satisfies a kind of weak distributivity. In case of a finite-dimensional Hilbert space H, the ortholattice L(H) is modular, that is, satisfies the following condition known as the modular law :